In addition to beignets, another wonderful Louisiana treat is boudin (pronounced "boo-da", with an almost silent "n" on the end). Usually it's pork sausage mixed with rice, green onions, cayenne pepper and other seasoning, all stuffed into a sausage skin.
You normally buy it cooked, wrapped in butcher paper. You don't eat the skin. You cut it into 4-inch or so segments and squeeze the filling 1) either directly into your mouth, or 2) onto a cracker, which you then add a dash of tabasco to before eating (recommended).
There's actually a pretty awesome boudin review site called The Boudin Link. We usually go to a place called Best Stop, though we tried Don's Specialty Meats last week and it was very nice as well. Also, there are different variations on traditional pork boudin. Last month I tried seafood boudin, which was stuffed with shrimp and crabmeat instead of pork. It wasn't quite as good as regular boudin, but it was still pretty tasty.
If you make you're way down to Louisiana, be sure to check this stuff out.